Real-world optimization problems often involve multiple conflicting objective functions to be optimized simultaneously. The optima to such multiobjective optimization problems are trade-off solutions constituting a so-called Pareto front. Practically, a few representative solutions are of interest for decision-making in lieu of the entire Pareto front as the latter is computationally and cognitively demanding to generate and analyze, respectively. However, finding a set of a few uniformly distributed solutions on the Pareto front is challenging for large-scale problems with irregularly-shaped Pareto fronts. We address this gap for a special type of problems inspired by a real-world case study in forest management. The proposed iterative Pareto representer uses an achievement scalarizing function to identify and prune certain search directions that are likely to yield duplicate or densely packed solutions. A subset selection technique is then used to identify the next search direction for achieving a relatively uniform distribution. Numerical experiments on 23 problems demonstrate the improved performance of the proposed approach over three alternate ones.
The state-of-the-art evolutionary algorithms (EAs), developed to solve constrained multi/many-objective optimization problems (M/MaOPs), mostly deal with deterministic design variables causing no uncertainty in their implementation. However, from a practical point of view, it is imperative to consider unavoidable uncertainties in implementing design variables and parameters. In the presence of hard constraints, a slight change in one or more variables may cause a feasible optimal solution to become infeasible upon implementation and result in a failure during operation. The literature suggests reliability-based techniques for solving such M/MaOPs to obtain a Reliable Front (ReF), rather than a Pareto-optimal front (PF). A ReF is usually either a part of the PF or a completely different set of trade-off solutions dominated by the deterministic PF. However, in the presence of decision-making, computing the complete ReF may not be necessary, as the focus would be to locate only the preferred part of the ReF, dictated by the objective preference information provided by a decision-maker (DM). The proposed approach incorporates DM's preferences and variable uncertainty information a priori. The proposed Reliability-based Multi-criteria Decision-making (ReMCDM) approach uses the hybrid mean value (HMV) method for constrained handling under variable uncertainties and R-NSGA-III for preference incorporation by DMs to conduct MCDM. Results obtained by the proposed method, implemented on several benchmark and realworld engineering examples, encourage future EMO research combining constraint handling, uncertainty in decision variables, and preference incorporation.
Coverage tasks have garnered significant interest in recent years due to their applications in fields such as environmental monitoring, search and rescue, and robotic exploration. Swarm robotics has emerged as a promising approach to tackle these challenges, leveraging collective behaviors to enhance efficiency. However, the effectiveness of swarm algorithms often hinges on the careful tuning of parameters, which can be influenced by varying environmental features. This study investigates the impact of these features on the performance of optimized collective motion in swarm robotics for solving multi-objective coverage problems. Through a comprehensive sensitivity analysis, we evaluate how changes in parameters-such as arena size, number of robots, obstacle density, and obstacle structure-affect swarm performance in solving coverage problems. The analysis focuses on key performance metrics across multiple objectives: coverage percentage, coverage time, robot connectivity, and collision rates. Our findings provide critical insights into the adaptability of swarm algorithms, highlighting the importance of environmental context in optimizing swarm efficacy across competing objectives. These results contribute to the development of more robust and adaptive swarm-based solutions for multi-objective coverage tasks.
In this paper, we propose an efficient optimization approach for multi-objective optimization problems (MOPs). The proposed utilizes an autoencoder-based surrogate model and gradient descent to search for Pareto optimal solutions. Evolutionary multi-objective optimization algorithms excel in finding diverse non-dominated solutions but often suffer from excessive execution times, particularly for real-world applications. Surrogate models offer a promising alternative by reducing the computational cost of objective function evaluations, and as such, have become the focus of increasing research interest. However, challenges persist in achieving accurate approximations and reducing surrogate model training times, limiting their practicality. To address this, we propose a method that uses an autoencoder with residual connections as surrogate models, introducing active learning to reduce sampling costs. The problem is then decomposed into multiple single-objective problems using weighted sum decomposition, and the solutions are optimized based on the approximate gradients established by the surrogate model. Evaluation experiments using the ZDT series and a human-powered aircraft design problem demonstrate that the proposed method effectively reduces sampling and training time, while achieving better approximation accuracy compared to existing surrogate methods. Furthermore, it achieves Pareto optimal fronts more quickly, while maintaining solution accuracy comparable to other representative evolutionary multiobjective optimization algorithms.
Most real-world optimization problems have multiple objectives and constraints. To address constrained multi-objective optimization problems (CMOPs), researchers have proposed many constrained evolutionary multi-objective optimization (EMO) algorithms. They usually evaluate the proposed constrained EMO algorithms on artificial CMOPs in the literature. As a result, some newly specialized constrained EMO algorithms are designed for those artificial problems. Our previous work demonstrated that an old EMO algorithm NSGA-II with a simple constraint handling mechanism can outperform some newly proposed algorithms on real-world CMOPs. In this paper, we further examine the performance of constrained EMO algorithms on artificial and real-world CMOPs. We also analyze the relationship between algorithms' performance and problems' properties.
